A224215 Number of nonnegative solutions to x^3 + y^3 + z^3 <= n^3.

1, 4, 11, 30, 66, 115, 200, 302, 441, 619, 829, 1085, 1395, 1771, 2200, 2666, 3228, 3843, 4564, 5351, 6185, 7143, 8158, 9349, 10526, 11934, 13375, 14896, 16652, 18381, 20370, 22411, 24629, 26963, 29406, 32101, 34840, 37766, 40920, 44164, 47587, 51200

Offset

0,2

Links

David A. Corneth, Table of n, a(n) for n = 0..1500

David A. Corneth, Pari prog

Formula

a(n) = [x^(n^3)] (1/(1 - x))*(Sum_{k>=0} x^(k^3))^3. - Ilya Gutkovskiy, Apr 20 2018

Example

For n=1, the four solutions are {0,0,0}, {0,0,1}, {0,1,0} and {1,0,0}, so a(1)=4.

Prog

(Python)
for a in range(99):
  n = a*a*a
  k = 0
  for x in range(99):
    s = x*x*x
    if s>n: break
    for y in range(99):
        sy = s + y*y*y
        if sy>n: break
        for z in range(99):
            sz = sy + z*z*z
            if sz>n: break
            k+=1
  print(str(k), end=', ')
(PARI) a(n) = n++; p = Pol((1/(1 - x))*sum(k=0, n, x^(k^3))^3 + O(x^(n^3))); polcoeff(p, (n-1)^3); \\ Michel Marcus, Apr 21 2018
(PARI) See PARI link \\ David A. Corneth, May 22 2018

Crossrefs

Cf. A224214.

Sequence in context: A361218 A024829 A296290 * A308082 A099065 A296262

Adjacent sequences: A224212 A224213 A224214 * A224216 A224217 A224218

Keyword

nonn

Author

Alex Ratushnyak, Apr 01 2013

Status

approved